A sports team of $11$ students is to be constituted, choosing atleast $5$ from class and atleast $5$ from Class If there are $20$ students in each of these classes, in how many ways can the team be constituted?
Updated On: Jul 6, 2022
$20 \times \, ^{20}C_{5}$
$^{20}C_{5} \times\, ^{20}C_{6}$
$2\times\, ^{20}P_{5} \times\, ^{20}P_{6}$
$2\times\,^{20}C_{5} \times\, ^{20}C_{6}$
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The Correct Option isD
Solution and Explanation
No. of students in each class $= 20$
We have to select atleast $5$ students from each class.
$\therefore$ No. of selection of sports team of $11$ students from each class is given in following table.
$\therefore$ Total number of ways of selecting a team of $11$ players
$=(^{20}C_{5} \times\, ^{20}C_{6}) +\, (^{20}C_{6} \times\, ^{20}C_{5}) $$= 2\times\, ^{20}C_{5} \times\,^{20}C_{6}$
